Coordinating the departure times of different line directions' of first and the last trains contributes to passengers' transferring. In this paper, a coordination optimization model (i.e., M1) referring to the first train's departure time is constructed firstly to minimize passengers' total originating waiting time and transfer waiting time for the first trains. Meanwhile, the other coordination optimization model (i.e., M2) of the last trains' departure time is built to reduce passengers' transfer waiting time for the last trains and inaccessible passenger volume of all origin-destination (OD) and improve passengers' accessible reliability for the last trains. Secondly, two genetic algorithms, in which a fixed-length binary-encoding string is designed according to the time interval between the first train departure time and the earliest service time of each line direction or between the last train departure time and the latest service time of each line direction, are designed to solve M1 and M2, respectively. Finally, the validity and rationality of M1, M2, and their solving genetic algorithms are verified with numerical analysis, in which the effects of the parameters in M1 and M2 on coordination optimization result are analyzed.
In order to improve train operation planning from the two perspectives of enterprise operating costs and passengers’ travel time, this paper proposes an integrated optimization model of three sub-problems, namely line planning, timetabling and rolling stock allocation for urban railway transit lines based on passengers’ travelling demands and the constraints of the urban rail line. The model features dwelling time at stations, turnaround operations at terminal stations, entering/exiting depot operations and an assignment for passengers’ travelling flow. We propose a solution method based on a metaheuristic method that simulates annealing to generate an optimal solution for the overall problem using MATLAB. Finally, we use the example of Xi’an metro line one to demonstrate the performance of the model.
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